Proyecto Salón Hogar

English Section


Math Page


An Approach




The Lessons

11.  Continuous versus discrete

12.  Limits

A sequence of rational numbers. The limit of a variable. The continuity of the x-axis.
The limit of a function at a point. Theorems on limits. Limits of polynomials.

13.  Continuous functions

The definition of "continuous at a point."

14.  The "limit" infinity ()

The definition of "becomes infinite." Limits of rational functions.

15.  The derivative

The slope of a tangent line to a curve. The difference quotient and the definition of the derivative. Differentiability. Notations for the derivative.

16.  Rules for derivatives

The derivative of a constant. The derivative of y = x. The product rule.
The power rule.
The derivative of the square root.

17.  The chain rule

The derivative of a function of a function.

18.  More rules for derivatives

The quotient rule.
Implicit differentiation.
The derivative of inverse functions.

19.  Velocity and rates of change

Instantaneous velocity.
Related rates.

10.  Maximum and minimum values

The turning points of a graph. Critical values.

11.  Applications of maximum and minimum values

12.  Derivatives of trigonometric functions

13.  Derivatives of inverse trigonometric functions

14.  Derivatives of exponential and logarithmic functions

Exponential growth. The system of natural logarithms. The general power rule.

15.  Evaluating e

  Appendix.   What is a number?
    The existence of the real numbers.